In Exercise 11 ofSection 6.3, we assumed that the contribution a female beetle of a
Chapter 7, Problem 13(choose chapter or problem)
In Exercise 11 ofSection 6.3, we assumed that the contribution a female beetle of a certain type made to the future years' beetle population could be expressed in terms ofthe matrix A = 0 1 2 0 0 0 1 3 6 0 0 where the entry in the /'th row and y'th column represents the probabilistic contribution of a beetle of age j onto the next year's female population of age i. a. Does the matrix A have any real eigenvalues? If so, determine them and any associated eigenvectors. b. If a sample of this species was needed for laboratory test purposes that would have a constant proportion in each age-group from year to year, what criteria could be imposed on the initial population to ensure thatthis requirement would be satisfied?
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